Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - 7.6 Exercises - Skill Practice - Page 520: 38

$$x=-8,\:x=-2$$

Using the rules of logarithms to solve the equation, we find: $$\log _4\left(\left(-x\right)\left(x+10\right)\right)=2 \\ \log _4\left(\left(-x\right)\left(x+10\right)\right)=\log _4\left(16\right) \\ -x\left(x+10\right)=16 \\ x=-8,\:x=-2$$ Checking for extraneous solutions, we see that both solutions valid.